If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=3x-2) and (g:\mathbb{R}\to\mathbb{R}) by (g(x)=\frac{x+2}{3}), what is the relation between (g) and (f)?

Correct answer: (g=f^{-1})

Step 1: From (y=3x-2), we get (x=\frac{y+2}{3}). Step 2: This matches the form of (g(y)), so (g) is the inverse function. Step 3: You can also verify an inverse by checking (f(g(x))=x) or (g(f(x))=x).